A method using state equation is one of useful methods to analyze Petri nets. An arbitrary nonnegative integer inhomogeneous solution for state equation Ax=b (A∈Z{sup}(m×n), b∈Z{sup}(m×l)) of Petri nets is represented by using generators of nonnegative integer homogeneous solutions and of nonnegative integer particular solutions. However, generators of nonnegative integer particular solutions are not well known. In this paper; the rank conditions, which are known as the method to distinguish between a minimal support T-invariant and an arbitrary T-invariant for Ax = b, are applied to the augmented system Ax = 0{sup}(m×l), where the incidence matrix is defined as A = A, -b∈Z{sup}(m×(n+1), and then a nonnegative integer particular solution for Ax = b is explicitly obtained. Moreover, the relations between particular solution structures and rank conditions are shown.
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